# 截角大十二面體

24
90

12個正十邊形{10}
12{5/2}+12{10}

2 5/3 | 5

10.10.5/2

(對偶多面體)

## 分類

1993年，茲維·喀拉·埃爾發表的論文《Uniform Solution for Uniform Polyhedra》中，將截角大十二面體編號為K42，表示其為一個二十面體對稱的多面體[3]，同一年，馬德爾參考茲維·喀拉·埃爾的分類方式，將截角大十二面體給予索引編號U37[4]。其也被考克斯特的論文收錄，並給予編號C47[5]。溫尼爾也在他的書《多面體模型》中將之給予編號W75[6]

## 性質

### 二面角

${\displaystyle {\text{Angle}}_{\left\{10\right\},\left\{10\right\}}=\cos ^{-1}{\frac {\sqrt {5}}{5}}\approx 63.434948823^{\circ }}$
${\displaystyle {\text{Angle}}_{\left\{10\right\},\left\{{^{5}}/{_{2}}\right\}}=\cos ^{-1}{\frac {-{\sqrt {5}}}{5}}\approx 116.565051177^{\circ }}$

### 頂點座標

${\displaystyle (\pm {\frac {1}{2}},0,\pm {\frac {5+{\sqrt {5}}}{4}})}$
${\displaystyle (\pm {\frac {5+{\sqrt {5}}}{4}},\pm {\frac {1}{2}},0)}$
${\displaystyle (0,\pm {\frac {5+{\sqrt {5}}}{4}},\pm {\frac {1}{2}})}$
${\displaystyle (\pm {\frac {1+{\sqrt {5}}}{4}},\pm {\frac {1}{2}},\pm {\frac {1+{\sqrt {5}}}{2}})}$
${\displaystyle (\pm {\frac {1+{\sqrt {5}}}{2}},\pm {\frac {1+{\sqrt {5}}}{4}},\pm {\frac {1}{2}})}$
${\displaystyle (\pm {\frac {1}{2}},\pm {\frac {1+{\sqrt {5}}}{2}},\pm {\frac {1+{\sqrt {5}}}{4}})}$
${\displaystyle (\pm {\frac {3+{\sqrt {5}}}{4}},\pm {\frac {{\sqrt {5}}\pm 1}{4}},\pm {\frac {3+{\sqrt {5}}}{4}})}$
${\displaystyle (\pm {\frac {3+{\sqrt {5}}}{4}},\pm {\frac {3+{\sqrt {5}}}{4}},\pm {\frac {{\sqrt {5}}\pm 1}{4}})}$
${\displaystyle (\pm {\frac {{\sqrt {5}}\pm 1}{4}},\pm {\frac {3+{\sqrt {5}}}{4}},\pm {\frac {3+{\sqrt {5}}}{4}})}$

## 參考文獻

1. ^
2. ^ Eric W. Weisstein. Truncated Great Dodecahedron. 密西根州立大學圖書館. （原始内容存档于2013-06-21）.
3. ^ Har'El, Z. Uniform Solution for Uniform Polyhedra. 页面存档备份，存于互联网档案馆, Geometriae Dedicata 47, 57-110, 1993. Zvi Har’El 页面存档备份，存于互联网档案馆, Kaleido software 页面存档备份，存于互联网档案馆, Images 页面存档备份，存于互联网档案馆, dual images 页面存档备份，存于互联网档案馆
4. ^ Mäder, R. E. Uniform Polyhedra. Mathematica J. 3, 48-57, 1993. [1]
5. ^ Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. Uniform polyhedra (PDF). Philosophical Transactions of the Royal Society A (皇家学会). 1954, 246 (916): 401–450. ISSN 0080-4614. JSTOR 91532. MR 0062446. doi:10.1098/rsta.1954.0003.
6. ^ . Polyhedron Models. Cambridge University Press. 1974. ISBN 0-521-09859-9.
7. ^ truncated great dodecahedron. bulatov.org. （原始内容存档于2016-03-26）.
8. ^ Self-Intersecting Truncated Regular Polyhedra: Truncated Great Dodecahedron. dmccooey.com. （原始内容存档于2017-03-12）.
9. ^ Data of Truncated Great Dodecahedron. dmccooey.com. （原始内容存档于2016-10-01）.
10. ^ compound of truncated great dodecahedron and small stellapentakisdodecahedron. bulatov.org. （原始内容存档于2016-09-06）.